A Note on the Security Number of Grid-Like Graphs

For any graph \( G = (V, E) \), a non-empty set \( S \subseteq V \) is \emph{secure} if and only if \( |N[X] \cap S| \geq |N[X] – S| \) for all \( X \subseteq S \). The cardinality of a minimum secure set in \( G \) is the security number of \( G \). In this note, we give a new proof for the \emph{security number} of grid-like graphs.